Trigonometry Examples

$\sin (90 + x)$

Step 1

Rearrange terms.

$\sin (x + 90)$

Step 2

Double negation

$\sin (x - (- 90))$

Step 3

Apply the difference of angles identity.

$\sin (x) \cos (- 90) - \cos (x) \sin (- 90)$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$\sin (x) (- \cos (90)) - \cos (x) \sin (- 90)$

Step 4.1.2

The exact value of $\cos (90)$ is $0$ .

$\sin (x) (- 0) - \cos (x) \sin (- 90)$

Step 4.1.3

Multiply $- 1$ by $0$ .

$\sin (x) \cdot 0 - \cos (x) \sin (- 90)$

Step 4.1.4

Multiply $\sin (x)$ by $0$ .

$0 - \cos (x) \sin (- 90)$

Step 4.1.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.

$0 - \cos (x) (- \sin (90))$

Step 4.1.6

The exact value of $\sin (90)$ is $1$ .

$0 - \cos (x) (- 1 \cdot 1)$

Step 4.1.7

Multiply $- 1$ by $1$ .

$0 - \cos (x) \cdot - 1$

Step 4.1.8

Multiply $- \cos (x) \cdot - 1$ .

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Step 4.1.8.1

Multiply $- 1$ by $- 1$ .

$0 + 1 \cos (x)$

Step 4.1.8.2

Multiply $\cos (x)$ by $1$ .

$0 + \cos (x)$

Step 4.2

Add $0$ and $\cos (x)$ .

$\cos (x)$